A parametric modeling of ionic channel current fluctuations using third-order statistics and its application to estimation of the kinetic parameters of single ionic channels

Digital processing of the current noise evoked by kainate in cerebellar granule cells

Current induced in cultured cerebellar granule cells by the bath application of kainate (500 microM) was measured using the conventional patch-clamp technique. Two different kinds of responses were observed after the agonist perfusion. Some cells exhibited small inward whole-cell currents: 116 +/- 40 pA (7 cells) at a clamp potential of -60 mV; in other cells, the agonist induced significantly larger currents: 420 +/- 35 pA (6 cells) at a clamp potential of -60 mV. The current flowing in the agonist-activated ionic channels was indirectly estimated by processing the fluctuations of whole-cell current by means of an original parametric method. Mean conductance of the underlying channels was then determined from the single-channel current estimated at different clamp potentials. In the cells exhibiting small inward currents, the mean conductance was equal to 0.5 +/- 0.2 pS (7 cells), whereas in the cells with large inward currents it was 3 +/- 0.4 pS (6 cells). This result gives a coherent explanation of the different kinds of responses observed at macroscopic level in the whole-cell current and confirms that kainate-activated channels can exhibit different levels of conductance.

Parameter estimation by reduced-order linear associative memory (ROLAM)

In a series of papers we have shown that nonlinear parameter estimation by linear association provides accurate estimates of the parameters in complex systems described by nonlinear differential equations even in the presence of additive white noise of considerable power. The technique is based on linearly associating the system's output with a set of parameter values spanning the region of interest. When an actual output is measured, the system's unknown parameters could be estimated by a matrix inversion. The size of the inverted matrix, being equal to the length of the output vector, poses a limiting factor upon the generalization of the technique. In this paper we propose a modification which requires the inversion of a matrix whose dimension equals the number of model parameters. The modified version is called reduced-order associative memory (ROLAM). The technique is applied to two complex lumped-parameter nonlinear models: the Van der Pol relaxation oscillator and the passive neuron model of the granule cells. Results validate ROLAM as a parameter-estimation tool which is especially suited in cases where the number of parameters is large, the number of samples in the observation signal is high, or when on-line parameter estimation is required. It is also shown that ROLAM provides an optimal parameter estimate in the special case of single-parameter nonlinear models.